During the Rosetta flyby at asteroid Lutetia the ROSINA instrument tried to detect a thin exosphere of the asteroid. Although the instrument is sensitive enough to detect even very tenuous gases at a density level of 1 cm−3 the Lutetia exosphere could not be unambiguously detected due to spacecraft outgassing, which was not constant because of the changing solar aspect angle. An upper limit for a water exosphere density at the flyby distance of 3160 km of (3.5±1.0)*103 cm−3 was deduced from the measurements.